Gravit. rotational energy related to KE

In summary, the gravitational potential energy of a system of two particles with identical masses orbiting in circles around their center of mass is equal to -2 times the total kinetic energy. This can be found by balancing the force on each particle with the centripetal acceleration to find the velocity.
  • #1
katewhitney
2
0
"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy.

Homework Equations


KE = 1/2 mv^2
U(potential) = -2U(kinetic)
grav. potential =
U=-GMm-r

The Attempt at a Solution


we're supposed to set 1/2mv^2 to the rotational gravitational energy -- but I think i have the wrong equation and I don't know where to go from here...
 
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  • #2
Welcome to PF!

katewhitney said:
"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy.

Hi kate! Welcome to PF! :smile:

Hint: find the force on each particle, and balance it with the centripetal acceleration to find v. :wink:
 

What is gravitational rotational energy?

Gravitational rotational energy is the kinetic energy associated with the rotation of an object due to the force of gravity acting on it. This type of energy is often seen in celestial bodies, such as planets and stars, as they rotate around their axis.

How is gravitational rotational energy related to kinetic energy?

Gravitational rotational energy is a form of kinetic energy, which is the energy an object possesses due to its motion. In this case, the motion is the rotation of the object caused by the force of gravity, thus making it a type of kinetic energy.

What factors affect the amount of gravitational rotational energy an object has?

The amount of gravitational rotational energy an object has is affected by its mass, radius, and the force of gravity acting upon it. Objects with larger masses or radii, or those experiencing stronger gravitational forces, will have more gravitational rotational energy.

Can gravitational rotational energy be converted into other forms of energy?

Yes, gravitational rotational energy can be converted into other forms of energy, such as heat or light. This is often seen in the case of celestial bodies, where the energy from their rotation can be converted into thermal energy, causing them to emit light and heat.

How is gravitational rotational energy calculated?

The formula for calculating gravitational rotational energy is E = 1/2Iω², where E is the energy, I is the moment of inertia (a measure of an object's resistance to rotation), and ω is the angular velocity (how fast the object is rotating). This formula takes into account the mass, size, and speed of the rotating object.

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